# DthetaphiTra: Mid/spr distance between trapezoidal fuzzy numbers In FuzzyStatTra: Statistical Methods for Trapezoidal Fuzzy Numbers

## Description

This function calculates the mid/spr distance between the trapezoidal fuzzy numbers contained in two matrixes, which should be given in the desired format. For this, the function first checks if the input matrixes R and S are in the correct form (tested by checkingTra).

## Usage

 1 DthetaphiTra(R, S, a = 1, b = 1, theta = 1/3) 

## Arguments

 R matrix of dimension r x 4 containing r trapezoidal fuzzy numbers characterized by their four values inf0,inf1,sup1,sup0. The function first calls checkingTra to check if the matrix R has the correct format. S matrix of dimension s x 4 containing s trapezoidal fuzzy numbers characterized by their four values inf0,inf1,sup1,sup0. The function first calls checkingTra to check if the matrix S has the correct format. a number >0, by default a=1. It is the first parameter of a beta distribution which corresponds to a weighting measure on [0,1]. b number >0, by default b=1. It is the second parameter of a beta distribution which corresponds to a weighting measure on [0,1]. theta number >0, by default theta=1/3. It is the weight of the spread in the mid/spr distance.

See examples

## Value

The function returns a matrix of dimension r x s containing the mid/spr distances between the trapezoidal fuzzy numbers of the matrix R and the trapezoidal fuzzy numbers of the matrix S.

## Note

In case you find (almost surely existing) bugs or have recommendations for improving the functions comments are welcome to the above mentioned mail addresses.

## Author(s)

Asun Lubiano <lubiano@uniovi.es>, Sara de la Rosa de Saa <rosasara@uniovi.es>

## References

[1] Lubiano, M.A.; Montenegro, M.; Sinova, B.; De la Rosa de Saa, S.; Gil, M.A.: Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications, European Journal of Operational Research 251, pp. 918-929 (2016)

checkingTra, Dthetaphi
 1 2 3 4 5 6 7 8 9 # Example 1: F=SimulCASE1(6) S=SimulCASE1(8) DthetaphiTra(F,S) # Example 2: F=matrix(c(1,1,0,2,3,4,5,6),nrow=2) S=SimulCASE1(8) DthetaphiTra(F,S,1,1,1)